The The Dynamics of a Prey-Predator Model with Infectious Disease in Prey: Role of Media Coverage

In this paper, an eco-epidemiological model with media coverage effect is proposed and studied. A prey-predator model with modified Leslie-Gower and functional response is studied. An -type of disease in prey is considered. The existence, uniqueness and boundedness of the solution of the model are discussed. The local and global stability of this system are carried out. The conditions for the persistence of all species are established. The local bifurcation in the model is studied. Finally, numerical simulations are conducted to illustrate the analytical results.

Effects of Immune Response and Time Delays in Models of Acute Myeloid Leukaemia

In this paper, we propose a general acute myeloid leukaemia (AML) model and introduce an immune response and time delays into this model to investigate their effects on the dynamics. Based on the existence, stability and local bifurcation of three types of equilibria, we show that the immune response is a best strategy for the control of the AML on the condition that the rates of proliferation and differentiation of the hematopoietic lineage exceed a threshold. In particular, a powerful immune response leads to bi-stability of the steady states, and a stronger response wipes out all the leukaemia cells. In addition, we further reveal that the time delays existing in the feedback regulation and immune response process induce a series of oscillations around the steady state, which shows that the leukaemia cells can hardly be eliminated. Our work in this paper aims to investigate the complex dynamics of this AML model with the immune response and time delays on the basis of mathematical models and numerical simulations, which may provide a theoretical guidance for the treatments of the AML.

Tip Trajectory Characteristics and Nonlinear Stability Analysis of Robotic Manipulator With Flexible Links-joints

An efficient and new dynamic model of two-link flexible manipulator connected and controlled by flexible joints i.e., prismatic and revolute pairs has been developed to explore the modal analysis to study tip-trajectory characteristics and subsequently investigate the nonlinear steady-state responses under harmonic motion at flexible joints. The governing equations including joint dynamics have been derived using extended Hamilton’s principle. Modal parameters have been graphically presented to highlight the influences of various system parameters on the determination of eigenfrequencies and eigenspectrums. Obtained reduced order equations have then used to study the trajectory characteristics of tip displacements, angular and actuator positions by imparting the appropriate actuator force and joint torque. Further, nonlinear studies have been carried out to compute the steady state responses and their stability and local bifurcation by using 2nd order method of multiple scales. Investigation of the influences of various design parameters on the nonlinear stability and local bifurcation of steady state responses have been demonstrated and those results have been found to be in good agreement with numerically obtained findings. The obtained results find very useful in the applications of long-reach robot manipulators performing complex operations assigning with translating and rotary motion together.

Global Bifurcation Structure of a Predator-Prey System with a Spatial Degeneracy and B-D Functional Response

In this paper, we investigate a predator-prey system with Beddington–DeAngelis (B-D) functional response in a spatially degenerate heterogeneous environment. First, for the case of the weak growth rate on the prey ( λ 1 Ω < a < λ 1 Ω 0 ), a priori estimates on any positive steady-state solutions are established by the comparison principle; two local bifurcation solution branches depending on the bifurcation parameter are obtained by local bifurcation theory. Moreover, the demonstrated two local bifurcation solution branches can be extended to a bounded global bifurcation curve by the global bifurcation theory. Second, for the case of the strong growth rate on the prey ( a > λ 1 Ω 0 ), a priori estimates on any positive steady-state solutions are obtained by applying reduction to absurdity and the set of positive steady-state solutions forms an unbounded global bifurcation curve by the global bifurcation theory. In the end, discussions on the difference of the solution properties between the traditional predator-prey system and the predator-prey system with a spatial degeneracy and B-D functional response are addressed.

On the Dynamics of an Eco-Epidemiological System Incorporating a Vertically Transmitted Infectious Disease

An eco-epidemiological system incorporating a vertically transmitted infectious disease is proposed and investigated. Micheal-Mentence type of harvesting is utilized to study the harvesting effort imposed on the predator. All the properties of the solution of the system are discussed. The dynamical behaviour of the system, involving local stability, global stability, and local bifurcation, is investigated. The work is finalized with the numerical simulation to observe the global behaviour of the solution.

The Effects of Harvesting on the Dynamics of a Leslie–Gower Model

In this paper, we study a Leslie–Gower predator-prey model with harvesting effects. We carry out local bifurcation analysis and stability analysis. Under certain conditions, the model is shown to undergo a supercritical Hopf bifurcation resulting in a stable limit cycle. Numerical simulations are presented to illustrate our theoretic results.